System and Method for Designing Curves

1. A system for designing curves, comprising: a user input unit supporting input from a user; a low-rank curve computation unit for computing low-rank curves, which are (n−1)-degree Bezier curves, and vector fields in response to the input from the user; a curve growth computation unit for computing a growth curve based on the low-rank curves; and a curve mixed computation unit for designing new curves by mixing curves inputted through the user input unit, the low-rank curves, and the growth curve.

2. The system of claim 1 , further comprising: an output unit for outputting result of the curve mixed computation unit.

3. The system of any one of claims 1 and 2 , wherein data inputted to the user input unit include two Bezier curves, lowest degree of the lowest-rank curve, growing method of each curve, control parameter of each curve growing method, extrapolation constant .beta., growth section, and growth interval.

4. The system of claim 3 , wherein the curve growth computation unit includes: a linear growth computer for performing computation in such a manner that a growth path is a straight line; a hierarchical linear growth computer for performing computation in such a manner that growth speed of adjacent low-rank curves is the same; a Bezier growth computer for computing a growth path of a curve d b (s,t) by taking points b i (t) of a low-rank curve corresponding to predetermined t as control points of the Bezier curves in the n-degree Bezier curve b n (t) defined by a parameter t where n is a natural number; and a spline growth computer for computing a growth path of 3-degree spline curve d s (s,t) passing a point b i (t) of each low-rank curve corresponding to the predetermined t.

5. The system of claim 4 , wherein the curve mixed computation unit includes: an extrapolation constant computer for computing an extrapolation constant corresponding to the β value; a primary interpolator for performing primary interpolation for the extrapolation and performing primary interpolation on the lowest-rank curve; a secondary interpolator for performing secondary interpolation on a primary interpolation result of the lowest-rank curve and on the growth curve; and a Bezier curve computer for converting degree of curve, computing spline control points, and performing output result.

6. A method for designing curves, comprising the steps of: inputting values including two Bezier curves, a lowest degree of the lowest-rank curve, a growing method of each curve, a control parameter of each curve growing method, an extrapolation constant β, a growth section, and a growth interval into a user input storage unit; storing the values in the user input storage unit; computing low-rank curves, which are (n−1)-degree Bezier curves, and vector field based on the input values with a low-rank curve computation unit; storing the low-rank curves and vector fields in a low-rank curve storage unit; computing a growth curve based on the low-rank curves; and designing new curves by mixing the input values, the low-rank curves and the growth curve.

7. The method of claim 6 , wherein the Bezier curves are converted into low-rank curves and vector field based on following equations 1 and 3: b n ⁡ ( t ) = b n - 1 ⁡ ( t ) + 2 ⁢ t ⁡ ( 1 - t ) ⁢ f n - 2 ⁡ ( t ) Equation ⁢ ⁢ 1 b n ⁡ ( t ) = b 1 ⁡ ( t ) + 2 ⁢ t ⁡ ( 1 - t ) ⁢ ∑ i = 0 n - 2 ⁢ f i ⁡ ( t ) Equation ⁢ ⁢ 3 where 1 denotes a parameter; n denotes a degree; b n (t) denotes a Bezier curve; and f i (t) denotes a vector field.

8. The method of claim 7 , wherein in the step of computing a growth curve, hierarchical linear growth, Bezier growth, and spline growth are computed based on the low-rank curves and the vector field.

9. The method of claim 8 , wherein the computation of hierarchical linear growth is defined as following equation 4: d p ⁡ ( s , t ) = b 1 ⁡ ( t ) + 2 ⁢ t ⁡ ( 1 - t ) ⁢ ∑ i = 0 n - 2 ⁢ α i ⁡ ( s ) ⁢ f i ⁡ ( t ) Equation ⁢ ⁢ 4 where d p (s,t) is a hierarchical linear growth curve; and a i (s) is a weight that vector field f i (t) contributes to the growth path.

10. The method of claim 8 , wherein the computation of Bezier growth is defined as following equation 6: d b ⁡ ( s , t ) = ∑ i = 0 n - 1 ⁢ b i + 1 ⁡ ( t ) ⁢ B i n - 1 ⁡ ( s ) = b 1 ⁡ ( t ) + 2 ⁢ t ⁡ ( 1 - t ) ⁢ ∑ i = 0 n - 1 ⁢ ∑ j = 0 i - 1 ⁢ f j ⁡ ( t ) ⁢ B i n - 1 ⁡ ( s ) Equation ⁢ ⁢ 6 where d b (s,t) is a Bezier growth curve; and a Bezier curve b(t) is ∑ i = 0 n ⁢ B i n ⁢ b i .

11. The method of claim 8 , wherein the computation of spline growth is defined as following equation 7: d s ⁡ ( s , t ) = ∑ i = 0 n - 1 ⁢ p i ⁢ N i , 3 ⁡ ( s ) Equation ⁢ ⁢ 7 where d p (s,t) denotes a spline growth curve; p i is d p (s,t)=b i (t) with respect to an arbitrary s i ; and N i,3 (S) is a 3-degree basis function of B-spline.

12. The method of any one of claims 6 to 11 , wherein the step of designing new curves includes the steps of: performing primary interpolation on a lowest-rank curve of the two Bezier curves; performing secondary interpolation onto a primary interpolation result and the computed growth curve; adjusting size of the primary interpolation with respect to the secondary interpolation result based on the primary interpolation result and the inputted extrapolation constant; and adjusting smoothness of curve with the lowest degree of the lowest-rank curve.